作者 |
標題: 極值 |
波斯貓 ![](email.gif)
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[ 36.232.180.86 ] |
發表於: 2024/8/13 上午 12:30:22
一方程組x^3-xyz=-5,y^3-xyz=2,z^3-xyz=21 求x^3+y^3+z^3之最小值
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小昭 ![](email.gif)
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[ 14.0.169.121 ] |
回覆於: 2024/8/18 上午 09:53:02
設t=xyz x^3=xyz-5=t-5 y^3=xyz+2=t+2 z^3=xyz+21=t+21 (x^3)(y^3)(z^3)=(t-5)(t+2)(t+21) t^3=t^3+18t^2-73t-210 18t^2-73t-210=0 (18t+35)(t-6)=0 t=-35/18或6 其中-35/18=-2+(1/18) _____ x^3+y^3+z^3 =(t-5)+(t+2)+(t+21) =3t+18 =3(-2+(1/18))+18或3(6)+18 =12+(1/6)或36 最小值=12+(1/6)
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小昭 ![](email.gif)
IP Address:
[ 14.0.169.121 ] |
回覆於: 2024/8/18 上午 09:59:11
另外 當t=-35/18時 x^3=t-5=-35/18-5=-125/18 x=-5/(18^(1/3)) y^3=t+2=-35/18+2=1/18 y=1/(18^(1/3)) z^3=t+21=-35/18+21=-343/18 z=-7/(18^(1/3))
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小昭 ![](email.gif)
IP Address:
[ 14.0.169.121 ] |
回覆於: 2024/8/18 上午 10:15:28
更正 z^3=t+21=-35/18+21=343/18 z=7/(18^(1/3))
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